# Function to generate the record count matrix for a single hospital
generate_record_count <- function(data) {
counts <- table(data[, "n_hi"])
result_matrix <- cbind(as.numeric(names(counts)), as.numeric(counts))
colnames(result_matrix) <- c("n_hi", "frequency")
return(result_matrix)
}
# Function to generate Z_hv matrix for a single hospital
generate_Zhv_matrix <- function(data) {
record_count_matrix <- generate_record_count(data)
diagonal_blocks <- list()
for (i in 1:nrow(record_count_matrix)) {
n_hi <- record_count_matrix[i, "n_hi"]
frequency <- record_count_matrix[i, "frequency"]
identity_block <- diag(frequency)
ones_vector <- matrix(1, nrow = n_hi, ncol = 1)
kronecker_product <- kronecker(identity_block, ones_vector)
diagonal_blocks[[i]] <- kronecker_product
}
big_matrix <- do.call(Matrix::bdiag, diagonal_blocks)
big_matrix <- cbind(1, big_matrix)
return(as.matrix(big_matrix))
}
# Function to get summary stats from each site for distributed LMM
lmm.get.summary3 <- function(Y = NULL, X = NULL, Z = NULL, id.site = NULL, weights = NULL) {
if (is.null(weights)) weights <- rep(1, length(Y))
X <- as.matrix(X)
id.site <- as.character(id.site)
id.site.uniq <- unique(id.site)
px <- ncol(X)
ShXYZ <- list()
for (h in seq_along(id.site.uniq)) {
sh <- id.site.uniq[h]
wth <- weights[id.site == sh]
Xh <- X[id.site == sh, ]
Yh <- Y[id.site == sh]
Zh <- Z[h][[1]]
ShX <- t(Xh * wth) %*% Xh
ShXZ <- t(Xh * wth) %*% Zh
ShXY <- t(Xh * wth) %*% Yh
ShZ <- t(Zh * wth) %*% Zh
ShZY <- t(Zh * wth) %*% Yh
ShY <- sum(Yh^2 * wth)
Nh <- sum(id.site == sh)
ShXYZ[[sh]] <- list(ShX = ShX, ShXZ = ShXZ, ShXY = ShXY,
ShZ = ShZ, ShZY = ShZY, ShY = ShY, Nh = Nh)
}
return(ShXYZ)
}
##############################
# different site different patients
# Parameters
H <- 5 # of sites
m_hosp <- sample(100:150, H, replace = T) # of patients (1k to 3k later)
px <- 9 # of covariates
p_bin <- 5 # of binary X
p_cont <- px - p_bin # of continuous X
beta0 = 5 # intercept
beta <- c(2, 4, 6, 8, 10, 3, 5, 7, 9) # Fixed effects for covariates
sigma_e <- 1 # error variance
sigma_u <- 3 # site-level variance
sigma_v_hosp <- runif(H, min = 1, max = 5) # Varying sigma_v by hospital
# Generate data
nn <- rep(m_hosp, times = 1) # Number of patients per hospital
id.hosp <- rep(1:H, times = m_hosp) # Hospital ID
id.pat <- sequence(nn) # Patient ID
n_visits <- sample(1:30, sum(nn), replace = TRUE) # number of visits of patients
# Expand hospital and patient IDs for visits
id.visit <- sequence(n_visits)
id.hosp.expanded <- rep(id.hosp, times = n_visits)
id.pat.expanded <- rep(id.pat, times = n_visits)
# Random effects
u_h <- rnorm(H, mean = 0, sd = sigma_u) # Hospital effects
v_hi <- rnorm(sum(nn), mean = 0, sd = rep(sigma_v_hosp, times = m_hosp)) # Patient effects varying by hospital
# Expansion of hospital effects
u_h_patient <- rep(u_h, times = m_hosp)
u_h_expanded <- rep(u_h_patient, times = n_visits)
# Expansion of patient effects
v_hi_expanded <- rep(v_hi, times = n_visits)
# covariates
X_bin <- matrix(rbinom(sum(n_visits) * p_bin, size = 1, prob = 0.3), nrow = sum(n_visits), ncol = p_bin)
X_cont <- matrix(rnorm(sum(n_visits) * p_cont, mean = 0, sd = 1), nrow = sum(n_visits), ncol = p_cont)
X_hij <- cbind(X_bin, X_cont) # Combine binary & continuous covariates
epsilon_hij <- rnorm(sum(n_visits), mean = 0, sd = sigma_e)
# Compute outcome
y_hij <- beta0 + X_hij %*% beta + u_h_expanded + v_hi_expanded + epsilon_hij
three_lvl_dat <- data.table(
site = id.hosp.expanded,
patient = id.pat.expanded,
visit = id.visit,
X_hij,
Y = y_hij
) %>% data.frame()
setnames(three_lvl_dat, c("site", "patient", "visit", paste0("X", 1:px), "Y"))
# Preprocessing
# Calculate the number of visits per patient per site
visit_count <- three_lvl_dat %>%
dplyr::group_by(site, patient) %>%
dplyr::summarise(total_visits = n(), .groups = "drop")
# Reorder data (as a preprocess probably)
rearranged_data <- merge(three_lvl_dat, visit_count, by = c("site", "patient")) %>%
arrange(site, total_visits, patient) %>%
mutate(site = factor(site))
# XYZ
Y <- rearranged_data$Y
X <- as.matrix(rearranged_data[, paste0("X", 1:px)])
X <- cbind(1, X)
Z <- list()
for(i in 1:H){
count_mat = rearranged_data %>%
filter(site == i) %>%
group_by(site, patient) %>%
dplyr::summarise(n_hi = n(), .groups = 'drop')
Z[[i]] <- (generate_Zhv_matrix(count_mat))
}
id.site <- rearranged_data$site
ShXYZ <- lmm.get.summary3(Y, X, Z, id.site)
source("DLMM_engine3RI.R")
bench::mark(lmm.fit3(Y = NULL, X = NULL, Z = NULL,
id.site = NULL, weights = NULL,
pooled = F, reml = T,
common.s2 = T,
ShXYZ = ShXYZ,
corstr = 'independence',
mypar.init = NULL))
default mypar.init (var comp) = 1 1 1 1 1 1
Normal exit from bobyqa The number of function evaluations used is 1739default mypar.init (var comp) = 1 1 1 1 1 1
Normal exit from bobyqa The number of function evaluations used is 1739
Warning: Some expressions had a GC in every iteration; so filtering is disabled.
fit03.dlmm = lmm.fit3(Y = NULL, X = NULL, Z = NULL,
id.site = NULL, weights = NULL,
pooled = F, reml = T,
common.s2 = T,
ShXYZ = ShXYZ, # only need summary stats
corstr = 'independence',
mypar.init = NULL)
default mypar.init (var comp) = 1 1 1 1 1 1
Normal exit from bobyqa The number of function evaluations used is 1739
fit03.dlmm$b
[,1]
2.427526
X1 2.030760
X2 4.025651
X3 6.009985
X4 8.027462
X5 9.964476
X6 3.002865
X7 5.003628
X8 7.003889
X9 8.990027
sqrt(fit03.dlmm$V)
[1] 2.006603 2.837770 3.293975 2.701197 2.025338 2.754136
sqrt(fit03.dlmm$s2)
[1] 0.9975977
true_beta = c(beta0, beta)
true_beta
[1] 5 2 4 6 8 10 3 5 7 9
true_sigma = c(sigma_u, sigma_v_hosp)
true_sigma
[1] 3.000000 2.733776 3.263261 2.339320 2.124376 2.726359
c(sigma_e)
[1] 1
plot(fit03.dlmm$b, true_beta)
points(fit03.dlmm$b[1], true_beta[1], col = "red")
abline(a = 0, b = 1, col = "blue", lwd = 2)

plot(sqrt(fit03.dlmm$V), true_sigma)
points(sqrt(fit03.dlmm$V)[1], true_sigma[1], col = "red")
abline(a = 0, b = 1, col = "blue", lwd = 2)

source("DLMM_Engine.R")
bench::mark(lmm.fit3(Y = NULL, X = NULL, Z = NULL,
id.site = NULL, weights = NULL,
pooled = F, reml = T,
common.s2 = T,
ShXYZ = ShXYZ,
corstr = 'independence',
mypar.init = NULL))
Default mypar.init (var comp) = 1 1 1 1 1 1
Normal exit from bobyqa The number of function evaluations used is 1182
Default mypar.init (var comp) = 1 1 1 1 1 1
Normal exit from bobyqa The number of function evaluations used is 1182
Warning: Some expressions had a GC in every iteration; so filtering is disabled.
fit03.dlmm = lmm.fit3(Y = NULL, X = NULL, Z = NULL,
id.site = NULL, weights = NULL,
pooled = F, reml = T,
common.s2 = T,
ShXYZ = ShXYZ, # only need summary stats
corstr = 'independence',
mypar.init = NULL)
Default mypar.init (var comp) = 1 1 1 1 1 1
Normal exit from bobyqa The number of function evaluations used is 1182
fit03.dlmm$b
[,1]
2.427516
X1 2.030760
X2 4.025651
X3 6.009985
X4 8.027462
X5 9.964476
X6 3.002865
X7 5.003628
X8 7.003889
X9 8.990027
sqrt(fit03.dlmm$V)
[1] 2.003896 2.837504 3.294069 2.701259 2.025409 2.753977
sqrt(fit03.dlmm$s2)
[1] 0.9975991
true_beta = c(beta0, beta)
true_beta
[1] 5 2 4 6 8 10 3 5 7 9
true_sigma = c(sigma_u, sigma_v_hosp)
true_sigma
[1] 3.000000 2.733776 3.263261 2.339320 2.124376 2.726359
c(sigma_e)
[1] 1
plot(fit03.dlmm$b, true_beta)
points(fit03.dlmm$b[1], true_beta[1], col = "red")
abline(a = 0, b = 1, col = "blue", lwd = 2)

plot(sqrt(fit03.dlmm$V), true_sigma)
points(sqrt(fit03.dlmm$V)[1], true_sigma[1], col = "red")
abline(a = 0, b = 1, col = "blue", lwd = 2)

source("DLMM_Engine_Efficient.R")
bench::mark(lmm.fit3(Y = NULL, X = NULL, Z = NULL,
id.site = NULL, weights = NULL,
pooled = F, reml = T,
common.s2 = T,
ShXYZ = ShXYZ,
corstr = 'independence',
mypar.init = NULL))
Default mypar.init (var comp) = 1 1 1 1 1 1
A <- matrix(runif(1024^2), nrow = 1024)
B <- matrix(runif(1024^2), nrow = 1024)
size = 1024
bench::mark(logdet <- log(det(diag(1, size) + t(A) %*% A %*% B)))
bench::mark(logdet <- as.numeric(determinant(diag(1, size) + t(A) %*% A %*% B, logarithm = TRUE)$modulus))
---
title: 'Codes'
output:
  html_notebook:
    code_folding: none
    highlight: textmate
  html_document:
    df_print: paged
---


```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = T, eval = T, cache = F, warning = T, message = T)
library(tidyverse)
library(lme4)
library(MASS)  
library(data.table)
library(gridExtra)
ggplot2::theme_set(ggplot2::theme_bw())
knitr::opts_chunk$set(out.width = "100%", fig.align = 'center')
set.seed(1918)
```


```{r}
# Function to generate the record count matrix for a single hospital
generate_record_count <- function(data) {
  counts <- table(data[, "n_hi"])
  result_matrix <- cbind(as.numeric(names(counts)), as.numeric(counts))
  colnames(result_matrix) <- c("n_hi", "frequency")
  return(result_matrix)
}

# Function to generate Z_hv matrix for a single hospital
generate_Zhv_matrix <- function(data) {
  record_count_matrix <- generate_record_count(data)
  diagonal_blocks <- list()

  for (i in 1:nrow(record_count_matrix)) {
    n_hi <- record_count_matrix[i, "n_hi"]
    frequency <- record_count_matrix[i, "frequency"]

    identity_block <- diag(frequency)
    ones_vector <- matrix(1, nrow = n_hi, ncol = 1)

    kronecker_product <- kronecker(identity_block, ones_vector)
    diagonal_blocks[[i]] <- kronecker_product
  }

  big_matrix <- do.call(Matrix::bdiag, diagonal_blocks)
  big_matrix <- cbind(1, big_matrix)
  return(as.matrix(big_matrix))
}

# Function to get summary stats from each site for distributed LMM
lmm.get.summary3 <- function(Y = NULL, X = NULL, Z = NULL, id.site = NULL, weights = NULL) {
  if (is.null(weights)) weights <- rep(1, length(Y))
  X <- as.matrix(X)
  id.site <- as.character(id.site)
  id.site.uniq <- unique(id.site)
  px <- ncol(X)

  ShXYZ <- list()
  for (h in seq_along(id.site.uniq)) {
    sh <- id.site.uniq[h]
    wth <- weights[id.site == sh]
    Xh <- X[id.site == sh, ]
    Yh <- Y[id.site == sh]
    Zh <- Z[h][[1]]

    ShX  <- t(Xh * wth) %*% Xh
    ShXZ <- t(Xh * wth) %*% Zh
    ShXY <- t(Xh * wth) %*% Yh
    ShZ  <- t(Zh * wth) %*% Zh
    ShZY <- t(Zh * wth) %*% Yh
    ShY  <- sum(Yh^2 * wth)
    Nh <- sum(id.site == sh)

    ShXYZ[[sh]] <- list(ShX = ShX, ShXZ = ShXZ, ShXY = ShXY,
                        ShZ = ShZ, ShZY = ShZY, ShY = ShY, Nh = Nh)
  }

  return(ShXYZ)
}
```


```{r}
##############################
# different site different patients

# Parameters
H <- 5  # of sites
m_hosp <- sample(50:100, H, replace = T) # of patients (1k to 3k later)


px <- 9  # of covariates
p_bin <- 5  # of binary X
p_cont <- px - p_bin  # of continuous X


beta0 = 5 # intercept
beta <- c(2, 4, 6, 8, 10, 3, 5, 7, 9)  # Fixed effects for covariates

sigma_e <- 1  # error variance
sigma_u <- 3 # site-level variance
sigma_v_hosp <- runif(H, min = 1, max = 5)  # Varying sigma_v by hospital


# Generate data
nn <- rep(m_hosp, times = 1)  # Number of patients per hospital
id.hosp <- rep(1:H, times = m_hosp)   # Hospital ID
id.pat <- sequence(nn)                # Patient ID
n_visits <- sample(1:30, sum(nn), replace = TRUE)  # number of visits of patients

# Expand hospital and patient IDs for visits
id.visit <- sequence(n_visits)
id.hosp.expanded <- rep(id.hosp, times = n_visits)
id.pat.expanded <- rep(id.pat, times = n_visits)

# Random effects
u_h <- rnorm(H, mean = 0, sd = sigma_u)  # Hospital effects
v_hi <- rnorm(sum(nn), mean = 0, sd = rep(sigma_v_hosp, times = m_hosp))  # Patient effects varying by hospital

# Expansion of hospital effects
u_h_patient <- rep(u_h, times = m_hosp)
u_h_expanded <- rep(u_h_patient, times = n_visits)

# Expansion of patient effects
v_hi_expanded <- rep(v_hi, times = n_visits)

# covariates
X_bin <- matrix(rbinom(sum(n_visits) * p_bin, size = 1, prob = 0.3), nrow = sum(n_visits), ncol = p_bin)
X_cont <- matrix(rnorm(sum(n_visits) * p_cont, mean = 0, sd = 1), nrow = sum(n_visits), ncol = p_cont)
X_hij <- cbind(X_bin, X_cont)  # Combine binary & continuous covariates

epsilon_hij <- rnorm(sum(n_visits), mean = 0, sd = sigma_e)

# Compute outcome
y_hij <- beta0 + X_hij %*% beta + u_h_expanded + v_hi_expanded + epsilon_hij

three_lvl_dat <- data.table(
  site = id.hosp.expanded,
  patient = id.pat.expanded,
  visit = id.visit,
  X_hij,
  Y = y_hij
) %>% data.frame()

setnames(three_lvl_dat, c("site", "patient", "visit", paste0("X", 1:px), "Y"))


# Preprocessing
# Calculate the number of visits per patient per site
visit_count <- three_lvl_dat %>%
  dplyr::group_by(site, patient) %>%
  dplyr::summarise(total_visits = n(), .groups = "drop")

# Reorder data (as a preprocess probably)
rearranged_data <- merge(three_lvl_dat, visit_count, by = c("site", "patient")) %>%
  arrange(site, total_visits, patient) %>%
  mutate(site = factor(site))


# XYZ
Y <- rearranged_data$Y
X <- as.matrix(rearranged_data[, paste0("X", 1:px)])
X <- cbind(1, X)
Z <- list()

for(i in 1:H){
  count_mat = rearranged_data %>%
                    filter(site == i) %>%
                    group_by(site, patient) %>%
                    dplyr::summarise(n_hi = n(), .groups = 'drop')

  Z[[i]] <- (generate_Zhv_matrix(count_mat))
}

id.site <- rearranged_data$site

ShXYZ <- lmm.get.summary3(Y, X, Z, id.site)
```


```{r}
source("DLMM_engine3RI.R")
bench::mark(lmm.fit3(Y = NULL, X = NULL, Z = NULL,
                     id.site = NULL, weights = NULL,
                     pooled = F, reml = T,
                     common.s2 = T,
                     ShXYZ = ShXYZ,
                     corstr = 'independence',
                     mypar.init = NULL))

fit03.dlmm = lmm.fit3(Y = NULL, X = NULL, Z = NULL,
                      id.site = NULL, weights = NULL,
                      pooled = F, reml = T,
                      common.s2 = T,
                      ShXYZ = ShXYZ,  # only need summary stats
                      corstr = 'independence',
                      mypar.init = NULL)


fit03.dlmm$b
sqrt(fit03.dlmm$V)
sqrt(fit03.dlmm$s2)



true_beta = c(beta0, beta)
true_beta
true_sigma = c(sigma_u, sigma_v_hosp)
true_sigma
c(sigma_e)


plot(fit03.dlmm$b, true_beta)
points(fit03.dlmm$b[1], true_beta[1], col = "red")
abline(a = 0, b = 1, col = "blue", lwd = 2)

plot(sqrt(fit03.dlmm$V), true_sigma)
points(sqrt(fit03.dlmm$V)[1], true_sigma[1], col = "red")
abline(a = 0, b = 1, col = "blue", lwd = 2)
```


```{r}
source("DLMM_Engine.R")
bench::mark(lmm.fit3(Y = NULL, X = NULL, Z = NULL,
                     id.site = NULL, weights = NULL,
                     pooled = F, reml = T,
                     common.s2 = T,
                     ShXYZ = ShXYZ,
                     corstr = 'independence',
                     mypar.init = NULL))


fit03.dlmm = lmm.fit3(Y = NULL, X = NULL, Z = NULL,
                      id.site = NULL, weights = NULL,
                      pooled = F, reml = T,
                      common.s2 = T,
                      ShXYZ = ShXYZ,  # only need summary stats
                      corstr = 'independence',
                      mypar.init = NULL)


fit03.dlmm$b
sqrt(fit03.dlmm$V)
sqrt(fit03.dlmm$s2)



true_beta = c(beta0, beta)
true_beta
true_sigma = c(sigma_u, sigma_v_hosp)
true_sigma
c(sigma_e)


plot(fit03.dlmm$b, true_beta)
points(fit03.dlmm$b[1], true_beta[1], col = "red")
abline(a = 0, b = 1, col = "blue", lwd = 2)

plot(sqrt(fit03.dlmm$V), true_sigma)
points(sqrt(fit03.dlmm$V)[1], true_sigma[1], col = "red")
abline(a = 0, b = 1, col = "blue", lwd = 2)
```




```{r}
source("DLMM_Engine_Efficient.R")
bench::mark(lmm.fit3(Y = NULL, X = NULL, Z = NULL,
                     id.site = NULL, weights = NULL,
                     pooled = F, reml = T,
                     common.s2 = T,
                     ShXYZ = ShXYZ,
                     corstr = 'independence',
                     mypar.init = NULL))


fit03.dlmm = lmm.fit3(Y = NULL, X = NULL, Z = NULL,
                      id.site = NULL, weights = NULL,
                      pooled = F, reml = T,
                      common.s2 = T,
                      ShXYZ = ShXYZ,  # only need summary stats
                      corstr = 'independence',
                      mypar.init = NULL)


fit03.dlmm$b
sqrt(fit03.dlmm$V)
sqrt(fit03.dlmm$s2)



true_beta = c(beta0, beta)
true_beta
true_sigma = c(sigma_u, sigma_v_hosp)
true_sigma
c(sigma_e)


plot(fit03.dlmm$b, true_beta)
points(fit03.dlmm$b[1], true_beta[1], col = "red")
abline(a = 0, b = 1, col = "blue", lwd = 2)

plot(sqrt(fit03.dlmm$V), true_sigma)
points(sqrt(fit03.dlmm$V)[1], true_sigma[1], col = "red")
abline(a = 0, b = 1, col = "blue", lwd = 2)
```



```{r, eval = F}
A <- matrix(runif(1024^2), nrow = 1024)
B <- matrix(runif(1024^2), nrow = 1024)
size = 1024

bench::mark(logdet <- log(det(diag(1, size) + t(A) %*% A %*% B)))
bench::mark(logdet <- as.numeric(determinant(diag(1, size) + t(A) %*% A %*% B, logarithm = TRUE)$modulus))
```


